On the other hand, as we know, the measurements for the cosmic microwave background (CMB) move us into the era of precision cosmology. However, since dark energy dominates the late universe, the measurements of CMB in the early universe have very weak constraints on the evolution of dark energy. It is necessary to combine with other late universe probes to break the degeneracy between cosmological parameters so that dark energy can get better constraints. Therefore, in this paper, the second point we want to investigate is what effect the combination of these three promising \(H(z)\)  measurements of the late universe and CMB of the early universe will have on breaking the degeneracies between cosmological parameters and what degree of constraint precision can be improved to dark energy. Here we consider five typical dark energy models, i.e., the \(\Lambda \) CDM model, the \(w\) CDM model, the Chevalliear-Polarski-Linder (CPL) model [1]}, [2]}, the holographic dark energy (HDE) model and a specific interacting dark energy model – I\(\Lambda \) CDM, to discuss these problems we are interested in.
